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A variant of Gaussian elimination called Gauss–Jordan elimination can be used for finding the inverse of a matrix, if it exists. If A is an n × n square matrix, then one can use row reduction to compute its inverse matrix, if it exists. First, the n × n identity matrix is augmented to the right of A, forming an n × 2n block matrix [A | I].
In mathematics, the Bruhat decomposition (introduced by François Bruhat for classical groups and by Claude Chevalley in general) = of certain algebraic groups = into cells can be regarded as a general expression of the principle of Gauss–Jordan elimination, which generically writes a matrix as a product of an upper triangular and lower triangular matrices—but with exceptional cases.
The reduced row echelon form of a matrix is unique and does not depend on the sequence of elementary row operations used to obtain it. The variant of Gaussian elimination that transforms a matrix to reduced row echelon form is sometimes called Gauss–Jordan elimination. A matrix is in column echelon form if its transpose is in row echelon form.
The Jordan normal form and the Jordan–Chevalley decomposition. Applicable to: square matrix A; Comment: the Jordan normal form generalizes the eigendecomposition to cases where there are repeated eigenvalues and cannot be diagonalized, the Jordan–Chevalley decomposition does this without choosing a basis.
The TI-83 Plus was designed in 1999 as an upgrade to the TI-83. The TI-83 Plus is one of TI's most popular calculators. The TI-83 Plus is one of TI's most popular calculators. It uses a Zilog Z80 microprocessor [ 3 ] running at 6 MHz , a 96×64 monochrome LCD screen, and 4 AAA batteries as well as backup CR1616 or CR1620 battery.
Wilhelm Jordan (1 March 1842, Ellwangen, Württemberg – 17 April 1899, Hanover) was a German geodesist who conducted surveys in Germany and Africa and founded the German geodesy journal. Biography [ edit ]
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